Complete the recursive formula of the geometric sequence $0.2\,,-1\,,\,5\,,-25,...$. $a(1)=$
The first term is $0.2$ and the common ratio is $-5$. ${\times (-5)\,\curvearrowright}$ ${\times (-5)\,\curvearrowright}$ ${\times (-5)\,\curvearrowright}$ $0.2,$ $-1,$ $5,$ $-25,...$ This is the recursive formula of $0.2\,,-1\,,\,5\,,-25,...$. $\begin{cases} a(1)=0.2 \\\\ a(n)=a(n-1)\cdot(-5) \end{cases}$